Three-Dimensional VLSI: a case study

The advantages of three-dimensional c~rcmts are studied by comparing sample three-dimensional reahzauons of certain common families of c~rcmts, namely, permutation networks, FFT circmts, and complete binary trees, with the famd~es' optunal two-dtmens~onal reahzatlons. These circuits are then used as building blocks to obtain efficient three-dimensional realizations of arbitrary circuits. The results obtained indicate (roughly) that bounds on area (both upper and lower) in the neighborhood of order n 2 m the two-dtmens~onal case translate to bounds on volume m the neighborhood of order n a/2 m the three-dimensional case. Moreover, several of the upper bounds are attainable using (idealized) realizations that have actwe devices on only one level and that use the third dimension only for wirerouting, such reahzauons place fewer demands on the fabrication technology. However, it is also shown that unrestricted use of the third dimension can y~eld reallzauons that are more conservative of volume (by the factor log~/2n) than any "one-actwe-level" reallzauon can be. Finally, examples are presented whereto two-dunenslonal reahzaUons reqmre dewce-to-dewce wire lengths as large as n/logn, whde eqmvalent three-dLmens~onal reahzatlons can get by w~th wire lengths not exceeding n ~/2. Thus, at least in the worst case, there are substantive savings from three-dLmens~onal circuit realizations, in both material (area versus volume) and tune (wire length) Categories and SubJect Descnptors B.2.m [Arithmetic and Logic Structures]: Miscellaneous; B.7 1 [Integrated Circuits]: Types and Design Styles--VLS1; F 2.2 [Analysis of Algorithms and Problem Complexity]. Nonnumencal Algorithms and Problems--routing and layout General Terms Design, Theory Addmonal

[1]  Jia-Wei Hong,et al.  Graphs that are Almost Binary Trees , 1982, SIAM J. Comput..

[2]  Jan Grinberg,et al.  Development Of A Three-Dimensional Circuit Integration Technology And Computer Architecture , 1981, Other Conferences.

[3]  Arnold L. Rosenberg,et al.  On Embedding Rectangular Grids in Square Grids , 1982, IEEE Transactions on Computers.

[4]  Z. Weinberg.  Polysilicon recrystallization by CO2 laser heating of SiO2 , 1981 .

[5]  Jean Vuillemin,et al.  A combinatorial limit to the computing power of V.L.S.I. circuits , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[6]  Arnold L. Rosenberg.  Three-Dimensional Integrated Circuitry , 1981 .

[7]  Jean Vuillemin,et al.  A Combinatorial Limit to the Computing Power of VLSI Circuits , 1983, IEEE Transactions on Computers.

[8]  Charles Seitz,et al.  In introduction to vlsi systems , 1980 .

[9]  Charles E. Leiserson,et al.  Area-Efficient Graph Layouts (for VLSI) , 1980, FOCS.

[10]  F. Leighton.  New lower bound techniques for VLSI , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[11]  Leslie G. Valiant,et al.  Universality considerations in VLSI circuits , 1981, IEEE Transactions on Computers.

[12]  R. Tarjan,et al.  A Separator Theorem for Planar Graphs , 1977 .

[13]  Lynn Conway,et al.  Introduction to VLSI systems , 1978 .

[14]  Charles E. Leiserson,et al.  Area-Efficient VLSI Computation , 1983 .

[15]  Leslie G. Valiant,et al.  Universal circuits (Preliminary Report) , 1976, STOC '76.

[16]  Journal of the Association for Computing Machinery , 1961, Nature.

[17]  Lawrence Snyder,et al.  Bounds on minimax edge length for complete binary trees , 1981, STOC '81.

[18]  V. Benes.  Optimal rearrangeable multistage connecting networks , 1964 .

[19]  T.C. Holloway,et al.  Characteristics of MOSFETs fabricated in laser-recrystallized polysilicon islands with a retaining wall structure on an insulating substrate , 1980, IEEE Electron Device Letters.